دانلود کتاب Linear Dynamical Systems

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Contents
1 Introduction
2 Single Degree of Freedom (SDOF) Systems
2.1 Newton\'s Second Law
2.2 Physical System
2.3 Equation of Motion
2.4 Time Domain Analysis
2.4.1 General Homogeneous Solution
2.4.2 General Homogeneous Solution (ζ<1)
2.4.2.1 Standard Form
2.4.2.2 Amplitude-Phase Representation
2.4.2.3 Damping Estimation
2.4.3 Particular Inhomogeneous Solution, Simple Forcing Functions
2.4.4 Particular Inhomogeneous Solution, Arbitrary Forcing Functions
2.4.5 Harmonic Force, Undamped System
2.4.5.1 Resonance Phenomenon
2.4.5.2 Beating Phenomenon
2.4.6 Harmonic Force, Damped System
2.4.6.1 Alternative Formulation
2.4.6.2 Dynamic Amplification Factor (DAF)
2.5 Frequency Domain Analysis
2.5.1 Fourier Series Representation of Forcing Functions
2.5.2 Steady-State Solution
2.6 Numerical Methods
2.6.1 Finite Difference (FD) Method
2.6.1.1 FD Approximations of Derivatives
2.6.1.2 FD Version of the Equation of Motion
2.6.2 Fourier Series (FS) Method
2.7 Applications
2.7.1 Response Spectra
2.7.2 Moving Loads
2.7.3 Coulomb Damping Model
2.8 Problems
References
3 Eigenvalue Problem
3.1 Systems of Linear Algebraic Equations
3.2 Eigenvalue Problem
3.2.1 Symmetric Matrices
3.2.2 Nonsymmetric Matrices
3.3 Problems
Reference
4 Multi-Degree of Freedom (MDOF) Systems
4.1 Physical System
4.2 Equations of Motion
4.3 Classical Modal Analysis
4.3.1 Modal Frequencies and Shapes
4.3.2 Properties of Modal Shapes and Frequencies
4.3.3 Approximate Calculation of Modal Frequencies
4.3.4 Proportional Damping
4.3.5 Displacement Vector Representations
4.4 Time Domain Analysis: Proportional Damping
4.4.1 Damped Systems: Forced Vibration
4.4.1.1 Initial Conditions for q(t)
4.4.1.2 System Displacement x(t)
4.4.1.3 Solution Uniqueness
4.4.2 Damped Systems: Free Vibration
4.4.3 Undamped Systems: Forced Vibration
4.4.4 Undamped Systems: Free Vibration
4.4.5 Earthquake Engineering
4.4.5.1 Seismic Ground Acceleration
4.4.5.2 Design Response Spectrum
4.4.6 Experimental Determination of Modal Frequencies
4.4.7 Torsional Vibration
4.5 Time Domain Analysis: Non-proportional Damping
4.5.1 State-Space Representation
4.5.2 Eigenvalues and Right/Left Eigenvectors
4.5.3 Properties of Eigenvalues and Right/Left Eigenvectors
4.5.4 Forced Vibration
4.5.5 Free Vibration
4.6 Frequency Domain Analysis
4.6.1 Fourier Series Representation of Vector-Valued Forcing Functions
4.6.2 Steady-State Solution: Proportional Damping
4.6.3 Steady-State Solution: Non-proportional Damping
4.6.4 Matrix Exponential
4.7 Problems
References
5 Continuous Systems
5.1 Flexural Beams
5.1.1 Physical System and Equations of Motion
5.1.2 Modal Shapes and Frequencies
5.1.3 Forced Vibration
5.1.4 Free Vibration
5.2 Shear Beams
5.2.1 Physical System and Equations of Motion
5.2.2 Modal Shapes and Frequencies
5.2.3 Forced Vibration
5.2.4 Free Vibration
5.3 Problems
References
Appendix A Taylor Series
Appendix B Linear Differential Equations
Appendix C Linear or Vector Spaces
Appendix D Generalized Eigenvectors
References
Index